The speed of light in diamond is 1.24 × 108 m s-1. Find its refractive index. (c = 3 × 108 m s-1)

μ = c/V = 3 × 108 / 1.24 × 108 = 2.42.

Light of frequency 5 × 1014 Hz enters water of refractive index 4/3. Find its wavelength in water.

V = c/μ = 2.25 × 108 m s-1; λ = V/f = 2.25 × 108 / 5 × 1014 = 4.5 × 10-7 m = 450 nm.

Refraction of Light at Plane Surfaces

ICSE Class 10 · Physics · Chapter 4

What this chapter covers

Refraction of light
Laws of refraction
Refractive index
Speed, wavelength and frequency in refraction
Experimental verification of the laws of refraction
Refraction through a glass block
Multiple images in a thick glass plate and a thick mirror
Refraction through a glass prism
Real and apparent depth
Total internal reflection
Total internal reflection in prisms
Applications of refraction and total internal reflection

Key definitions

Refraction is the change in the direction of a ray of light when it passes obliquely from one transparent medium into another in which its speed is different.

Angle of incidence is the angle between the incident ray and the normal at the point of incidence, and it is written as i.

Angle of refraction is the angle between the refracted ray and the normal at the point of incidence, and it is written as r.

An optically denser medium is a medium in which light travels more slowly than in the medium it is being compared with, and the other medium is called the optically rarer medium.

The first law of refraction is that the incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.

The second law of refraction is that for a given pair of media and light of a given colour, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant.

Absolute refractive index is the ratio of the speed of light in vacuum to the speed of light in the given medium.

Relative refractive index is the ratio of the speed of light in the first medium to the speed of light in the second medium, for light passing from the first medium into the second.

Emergent ray is the name given to the ray that leaves the second surface of a glass block or prism after the second refraction.

Angle of emergence is the angle between the emergent ray and the normal at the point of emergence, and it is written as e.

Lateral displacement is the perpendicular distance between the incident ray produced forward and the emergent ray when light passes through a parallel-sided glass block.

Refracting surfaces are the two plane faces of a prism through which light enters and leaves.

Key points

Refraction is the change in direction of light passing obliquely from one medium into another; it is caused by the change in the speed of light.
At every boundary light is partly reflected and partly refracted.
Rarer to denser: the ray bends towards the normal; denser to rarer: away from the normal; along the normal: no bending.
Laws of refraction: incident ray, refracted ray and normal lie in one plane; sin i/sin r = μ, a constant (Snell's law).
Refractive index μ = c/V = λ_air/λ_medium; it has no unit; ₁μ₂ = μ₂/μ₁ and _gμ_a = 1/_aμ_g.
Speed of light: vacuum and air 3 × 10⁸, water 2.25 × 10⁸, glass 2 × 10⁸ m s^-1; μ: water 1.33, glass 1.5, diamond 2.42.
μ depends on the medium, the colour of light and the temperature.
On refraction, speed and wavelength change but frequency stays the same; V = fλ.
A ray passes undeviated if it falls along the normal or if both media have the same refractive index.
The laws are verified by tracing rays through a glass block with pins: sin i/sin r stays constant.
A parallel-sided glass block gives an emergent ray parallel to the incident ray but laterally displaced; the displacement grows with thickness, angle of incidence and refractive index.
A thick mirror forms multiple images; the second is the brightest.
Prism: r₁ + r₂ = A and i₁ + i₂ = A + δ; the ray bends towards the base; deviation is least when the ray passes symmetrically.
μ = real depth/apparent depth; objects under water appear raised, and a stick in water appears bent.
Total internal reflection needs light going from denser to rarer and i > C; μ = 1/sin C; C is about 48.6° for water, 42° for glass and 24.4° for diamond.

Questions answered

Define refraction of light. What is its cause?

Refraction is the change in the direction of a ray of light when it passes obliquely from one transparent medium into another. It is caused by the change in the speed of light from one medium to the other.

State the two laws of refraction.

(i) The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane. (ii) For a given pair of media and light of a given colour, sin i/sin r is a constant, the refractive index of the second medium with respect to the first (Snell's law).

Kerosene is less dense than water but is said to be optically denser. Explain.

Optical density depends on the speed of light, not on mass per unit volume. Light travels more slowly in kerosene than in water, so kerosene has the greater refractive index and is optically denser.

Which of speed, wavelength and frequency of light change when it passes from air into glass? Give a reason for the one that does not change.

Speed and wavelength decrease. Frequency does not change, because it is fixed by the source; the number of waves crossing the boundary each second must be the same on both sides.

State two conditions under which a ray passes from one medium into another without deviation.

(i) It falls along the normal, at i = 0°. (ii) The two media have the same refractive index.

The speed of light in diamond is 1.24 × 10⁸ m s^-1. Find its refractive index. (c = 3 × 10⁸ m s^-1)

μ = c/V = 3 × 10⁸ / 1.24 × 10⁸ = 2.42.

Light of frequency 5 × 10¹⁴ Hz enters water of refractive index 4/3. Find its wavelength in water.

V = c/μ = 2.25 × 10⁸ m s^-1; λ = V/f = 2.25 × 10⁸ / 5 × 10¹⁴ = 4.5 × 10^-7 m = 450 nm.

Why is the emergent ray from a rectangular glass block parallel to the incident ray? Name two factors on which the lateral displacement depends.

The two faces are parallel, so the angle inside the glass at the second face equals the angle of refraction at the first; by reversibility the angle of emergence equals the angle of incidence. Lateral displacement increases with the thickness of the block and with the angle of incidence (it also depends on the refractive index and the colour of light).

Past board exam questions

ICSE 2027 sample paper · 1 mark

If red, blue, green and yellow lights are allowed to enter the same glass block with the same angle of incidence (∠i), then for which colour will the angle of deviation be the greatest?

blue
green
yellow
red

Show answer

blue

ICSE 2026 board paper · 1 mark

A ray of light passes from medium A into medium B. In medium A, the incident ray makes an angle of 30° with the surface separating the two media; in medium B, the refracted ray makes an angle of 45° with the surface. The refractive index of medium B with respect to medium A (_Aμ_B) is:

(sin 45^°)/(sin 30^°)
(sin 30^°)/(sin 45^°)
(sin 45^°)/(sin 60^°)
(sin 60^°)/(sin 45^°)

Show answer

(sin 60^°)/(sin 45^°)

ICSE 2026 sample paper · 1 mark

When objects are viewed through the rising heat of a campfire they appear to shimmer. The optical phenomenon responsible for this effect is:

refraction
reflection
scattering
total internal reflection

Show answer

refraction

ICSE 2026 sample paper · 3 marks

Advanced optical sensors in air-to-air missiles use fiber optic cables to transmit light signals with minimal loss. This relies on a physical phenomenon that confines light within the fibers, making the system very dependable for guiding the missile precisely. (a) Name the optical phenomenon that allows light signals to remain confined within the fiber optic cables during transmission. (b) Explain the two main conditions necessary for this phenomenon to occur.

Show answer

(a) Total internal reflection. (b) 1. Light must travel from an optically denser medium to an optically rarer medium (from the core of the fibre towards the cladding/outer surface). 2. The angle of incidence at the boundary must be greater than the critical angle for the pair of media.

ICSE 2026 sample paper · 3 marks

A fish in a tank and its image are seen on the surface of water: the fish is in the water and its inverted image is seen on the water surface above it, when viewed from below the surface. (a) Name the phenomenon responsible for the formation of this image. (b) A double convex lens with refractive index µ₁ is placed inside two liquids of refractive indices µ₂ and µ₃ as described below. The refractive indices are such that µ₂ > µ₁ and µ₁ > µ₃. Figure a: the lens is placed in Liquid 1 (µ₃). Figure b: the lens is placed in Liquid 2 (µ₂). How would a parallel incident beam of light refract when it comes out of the lens in each of the cases described above? (1) in Figure a. (2) in Figure b.

Show answer

(a) Total internal reflection (light from the fish meets the water–air surface at an angle greater than the critical angle and is reflected back into the water). (b) (1) Figure a: the lens is optically denser than the surrounding liquid (µ₁ > µ₃), so it behaves as a converging lens — the parallel beam converges. (2) Figure b: the lens is optically rarer than the surrounding liquid (µ₁ < µ₂), so it behaves as a diverging lens — the parallel beam diverges.

ICSE 2026 board paper · 3 marks

A monochromatic ray strikes the surface of identical prisms (A, B and C) at different angles of incidence. Their refracted rays are described below. In each prism, the ray enters through the left face; the dotted normal to that face slopes down towards the right, into the prism. Prism A: the refracted ray inside the prism slopes downwards, towards the base, as it goes to the right face. Prism B: the refracted ray inside the prism slopes upwards, towards the apex, as it goes to the right face. Prism C: the refracted ray inside the prism is parallel to the base. Study the path of these refracted rays and identify in which of the diagrams: (a) the angle of incidence is maximum. (b) the angle of incidence is minimum. (c) the angle of incidence is equal to the angle of emergence.

Show answer

(a) B — its refracted ray makes the largest angle with the normal (largest angle of refraction), so the angle of incidence is the largest. (b) A — its refracted ray is closest to the normal (smallest angle of refraction), so the angle of incidence is the smallest. (c) C — the refracted ray passes parallel to the base, the position of minimum deviation, in which the angle of incidence equals the angle of emergence.

ICSE 2026 sample paper · 3 marks

A scientist lowers a metallic ruler vertically into a transparent oil tank. The ruler touches an object placed at the bottom of the tank and gets wet up to the 25 cm mark. If the refractive index of the glycerin is 1.25: (a) up to which mark will the ruler get wet, if the scientist lowers it up to the image of the object? (b) how will this length in (a) change if another liquid of µ>1.25 is used?

Show answer

(a) Real depth = 25 cm, µ = 1.25 Apparent depth = real depth ÷ µ = 25 ÷ 1.25 = 20 cm The image is 20 cm below the surface, so the ruler gets wet up to the 20 cm mark. (b) The length will decrease, since apparent depth = real depth/µ is smaller for a larger µ.

ICSE 2026 board paper · 3 marks

A ray of light enters a glass block from air and comes out from the opposite surface. If the angle of refraction at the first surface is not the same as the angle of incidence at the second surface, then: (a) What is the product of the ratio (sin i)/(sin r) at the first surface and at the second surface? (b) State whether the opposite surfaces are parallel or not parallel. (c) How did you reach the conclusion in (b) above?

Show answer

(a) 1. At the first surface (sin i)/(sin r) = _aμ_g and at the second surface it is _gμ_a = frac1_aμ_g; their product is _aμ_g × _gμ_a = 1. (b) Not parallel. (c) If the two surfaces were parallel, the normals at the two points would be parallel, and the angle of refraction at the first surface would equal the angle of incidence at the second surface (alternate angles). Since these angles are not equal, the surfaces are not parallel.